Construction Of Wavelet Bases That Mimic The Behaviour Of Some Given Operator
نویسندگان
چکیده
Probably the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new families of wavelets that behave like an arbitrary scale-covariant operator. Our extension is general and includes many known wavelet bases. At the same time, the method takes advantage a fast filterbank decomposition-reconstruction algorithm. We give necessary conditions for the scale-covariant operator to admit our wavelet construction, and we provide examples of new wavelets that can be obtained with our method.
منابع مشابه
On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
In the present paper, we introduce the two-wavelet localization operator for the square integrable representation of a homogeneous space with respect to a relatively invariant measure. We show that it is a bounded linear operator. We investigate some properties of the two-wavelet localization operator and show that it is a compact operator and is contained in a...
متن کاملOperator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملWavelets with Complementary Boundary Conditions { Function Spaces on the
This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on part of the boundary. The essential point is that the primal and dual wavelets satisfy certain corresponding complementary boundary conditions. These results form the key ingredients of the con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007